1、第第9 9章章 非线性控制系统非线性控制系统234非线性特性非线性特性线性化系统线性化系统客观非线性客观非线性人为非线性人为非线性非本质非线性非本质非线性本质非线性本质非线性非线性系统非线性系统，5671()0sgn()1()0 x tx tx t()()()sgn()()kx tx tay tkax tx ta8a 死区宽度死区宽度k 线性输出斜率线性输出斜率0()()()sgn()()x tay tk x tax tx ta9()()0()()()0sgn()()0k x tay ty tk x tay tMx ty t2a 间隙宽度间隙宽度k 线性段斜率线性段斜率M 常数常数1021()
2、()()()()k x tx tay tk x tx tak1、k2 变增益特变增益特性的斜率性的斜率a 切换点切换点110(),()00(),()0()sgn()()(),()0(),()0max ta x tax tma x ty tMx tx taMx tma x tMx tma x t 12131415160),(xxfx),(xxfx x),(21221xxfxxx)(tx x 1718),(),(/xxxxxfxxdtdxdtxddxxd 19),(),(/xxxxxfxxdtdxdtxddxxd x),(),(xxfxxf),(),(xxfxxfx),(),(xxfxxf20(a
3、)稳定极限环稳定极限环(b)(c)半稳定极限环半稳定极限环(d)不稳定极限环不稳定极限环210Tcc1ccT 22220nnxxx令令 ，得，得系统奇点为系统奇点为(0，0)。2(,)200nnf x xxxx0222nnss2,1s23022xxxnn xxxxxnn22),(xxnn221)1(22,1n22nndxdx 022xxxnn)1(22,1n242526(,)0 xf x x(,)(,)(,)(,)()()eeeeeeeex xx xfff x xf x xxxxxxx(,)f x x(,)(,)eeeex xx xffxxxxx 27025.02xxxx 025.02xxx
4、0 x 10ex10ex22ex 20ex(0,0)2fx(2,0)0.5fx(2,0)2fx(0,0)0.5fx0.520 xxx 0.520 xxx 280.520 xxx 025.02ss39.125.02,1js025.02ss69.1,19.12,1s0.520 xxx 2930)(tx 313200UdUd21222020UcUc 00UU3302xxn xxdxxdn2222)(Axxn20202)(xxAn34x 02xxn)cos()(tAtxn222)(Axxn20202)(xxAn)sin()(tAdtdxtxnn35(,)0 xf x x(,)dxf x xdxx(,)
5、xg x36xxxdxxd/xax110 xxx 372/(1)/x xxxxx 21xxax2(1)0 xxxx383940TccKubeaueeaeea(0)0c41TeeKbTrreaTeeKeTrreaTeeKbTrrea 000TeeKbeaTeeKeeaTeeKbea 420TeeKbea 1KbeT/0de deeKb0TeeKeea(0,0)1,20.51.94sj 430TeeKbea 1KbeT/0de deeKb(,0)R(0)(0)(0)ercR(0)(0)(0)0erc44000TeeKbVeaTeeKeVeaTeeKbVea 0()r tRV t0(/,0)VK0e
6、KbV0eKbV 01.2VKb(0.3,0)00.4VKb(0.1,0)00.8VKb(0.2,0)TeeKbTrreaTeeKeTrreaTeeKbTrrea 4546(0)0,(0)0ccTccKu12k eeauk eea47TccKu12k eeauk eea12TeeKk eTrreaTeeKk eTrrea erc480)()(trtr 0)0(e Re)0(02eKkeeT 01eKkeeT()1()r tRt49505110TeeKk eV 20TeeKk eV 0()r tV0(0)eV(0)eR0)(tr 0()r tRV t525354555657580011()(co
7、ssin)sin()22nnnnnnAAy tAn tBn tYn t2001()()Ay t dt201()cos()nAy tn tdt201()sin()nBy tn tdt22nnnYABarctannnnAB()sinx tAt59001111111()(cossin)sin()22()cossinsin()nnnnnnAAy tAn tBn tYn ty tAtBtYt2101()cosAy ttd t2101()sinBy ttd t21211BAX111arctanAB1111()YBjAN AAA6061arcsinaAsin0()sinkAtty tkatkAtt6202/
8、21sinsin4ttdKattdKAB2)(1arcsin2AaAaAaKAttdtyAcos)(1201ttdtyBsin)(1201sin0()sinkAtty tkatkAtt63(sin)02()()2(sin)k Ataty tk Aatk Atat2arcsin 1aA64201)(cos)sin(2ttdatAKA/22()cos()K Aatdt/22(sin)cos()K Atatdt 14AaKattdtyAcos)(1201ttdtyBsin)(1201(sin)02()()2(sin)k Ataty tk Aatk Atat65)21()21(2)21arcsin(21AaAaAaAaKAB222arcsin(1)2(1)(1)24()()KaaaaAAAAKaaajAaAAA11()BAN AjAA666768697071/cab k727374)()(1)()()()()(jGANjGANjRjCj0)()(1jGAN)(1)(ANjG00()sinx tAt757677787921111arcsin4)(1AAAAN80501)(Re)(150jGAN8182838485
